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Level 636

Maclaurin Taylor Series


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1/1-x
1+x+x^2+...+x^n+...
1+x+x^2+...+x^n+...
1/1-x
1/1-x
0 sigma x^n x<1
1/1+x
1-x+x^2-...+(-x)^n+...
1-x+x^2-...+(-x)^n+...
1/1+x
1/1+x
0 sigma (-1)^n*x^n x<1
e^x
1+x+x^2/2!+...+x^n/n!+...
1+x+x^2/2!+...+x^n/n!+...
e^x
e^x
0 sigma x^n/n! all real
sin(x)
x-x^3/3!+x^5/5!-...+(-1)^n*(x^2n+1)/(2n+1)!+...
x-x^3/3!+x^5/5!-...+(-1)^n*(x^2n+1)/(2n+1)!+...
sin(x)
sin(x)
0 sigma (-1)^n*(x^2n+1)/(2n+1)! all real
cos(x)
1-x^2/2!+x^4/4!-...+(-1)^n*(x^2n)/(2n)!+...
1-x^2/2!+x^4/4!-...+(-1)^n*(x^2n)/(2n)!+...
cos(x)
cos(x)
0 sigma (-1)^n*(x^2n)/(2n)! all real
ln(1+x)
x-x^2/2+x^3/3-...+(-1)^(n-1)*(x^n)/n+...
x-x^2/2+x^3/3-...+(-1)^(n-1)*(x^n)/n+...
ln(1+x)
ln(1+x)
1 sigma (-1)^(n-1)*(x^n)/n -1<x≤1
arctan(x)
x-x^3/3+x^5/5-...+(-1)^n*(x^2n+1)/(2n+1)+...
x-x^3/3+x^5/5-...+(-1)^n*(x^2n+1)/(2n+1)+...
arctan(x)
arctan(x)
0 sigma (-1)^n*(x^2n+1)/(2n+1) x≤1